May 6, 2009 - Density-functional calculations show that, depending on the anion size, hydrogen in anion vacancies of various II-VI semiconductors can be ...
PHYSICAL REVIEW B 79, 205201 共2009兲
Hydrogen in anion vacancies of semiconductors Mao-Hua Du and David J. Singh Materials Science and Technology Division and Center for Radiation Detection Materials and Systems, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 共Received 16 December 2008; revised manuscript received 8 April 2009; published 6 May 2009兲 Density-functional calculations show that, depending on the anion size, hydrogen in anion vacancies of various II-VI semiconductors can be either twofold or fourfold coordinated and has either amphoteric or shallow donor character. In general, the multicoordination of hydrogen in an anion vacancy is the indication of an anionic H, H− ion, in the relatively ionic environment. In more covalent semiconductors, H would form a single cation-H bond in the anion vacancy. DOI: 10.1103/PhysRevB.79.205201
PACS number共s兲: 61.72.J⫺, 61.72.S⫺, 71.55.Gs
I. INTRODUCTION
Hydrogen is an important impurity in many semiconductors. It can passivate electrically active impurities and defects. It can also provide conductivity directly by acting as a shallow donor1 or indirectly as a codopant by boosting the concentration of other shallow dopants.2,3 The interaction between hydrogen and vacancies in semiconductors has been extensively studied for decades. Typically, hydrogen can terminate the dangling bonds around a vacancy, thereby partially or completely passivating the vacancy. However, it has been shown recently by density-functional calculations that hydrogen in anion vacancies 共Vanion兲 of many semiconductors, such as ZnO,4 MgO,4 InN,5 SnO2,6 and GaN,7 acts as an unintentional shallow donor, providing n-type conductivity to the materials. Furthermore, the hydrogen is found to be located near the center of the vacancy and coordinated to multiple nearest-neighbor cations. The multicoordination of the hydrogen in anion vacancies has led to discussion of the nature of chemical bonding around the hydrogen.4,8 A multicenter covalent bonding model was initially proposed.4,5 However, the electronic structural analyses showed that the hydrogen in the O vacancy of ZnO is anionic, i.e., the H− ion.8 The H− configuration is stabilized by the ionic bonding with the host ionic matrix rather than by the multicenter covalent bond. The single-electron donor character of VO-H is simply the result of replacing the O2− ion with the H− ion. In the ionic crystals, hydrogen is known to exist as H− ions in anion vacancies, e.g., the U center in alkali halides.9–11 It may be noted that the multicoordination of H found in recent calculations all exists in crystals of relatively high ionicity, e.g., ZnO, MgO, InN, SnO2, and GaN. This may be explained by the fact that H is stabilized by the Ewald field of the ionic matrix and thus its coordination number is not constrained by the number of available electron pairs, which is only essential for the bonding in covalent materials. Driven by the Coulomb attraction, H− would approach the cation as close as possible until the electronic shell overlap between the cation and H− is large enough to cause repulsion. It may thus be expected that H− would stay in the center of the anion vacancy if the anion size is small and the cation size is big but would move off center if the anion size 1098-0121/2009/79共20兲/205201共6兲
becomes large. We show by density-functional calculations that, in ZnX 共X = S, Se, and Te兲 and CdX 共X = S and Te兲, indeed, H moves off center but remains in the multicoordinated structure 共i.e., twofold coordination兲. The calculated H local vibration modes 共LVMs兲 are in good agreement with the experimental results, thus supporting the proposed H structures. H in anion vacancies is found to be amphoteric in all the II-VI semiconductors we have studied except the oxides. II. METHOD
We performed calculations based on density-functional theory within the local-density approximation 共LDA兲, as implemented in VASP.12 The electron-ion interactions are described by projector augmented wave pseudopotentials.13 The valence wave functions are expanded in a plane-wave basis with cutoff energy of 400 eV. All the calculations were performed using 64-atom cubic cells. A 2 ⫻ 2 ⫻ 2 grid was used for the k-point sampling of Brillouin zone. All the atoms were relaxed to minimize the Feynman-Hellmann forces to below 0.02 eV/ Å. We used zinc-blende structures for all the semiconductors under study. The calculated lattice constants of these materials are compared with the experimental results in Table I. The methods for calculating the transition energy levels can be found in Ref. 14. III. RESULTS
We have considered all the possible coordination numbers for the hydrogen in the anion vacancies of the semiconducTABLE I. The LDA lattice constants compared with the experimental values at room temperature 共in Ref. 28兲. The zine-blende structure is adopted for all the semiconductors listed in this table. All units are in Å.
ZnO ZnS ZnSe ZnTe CdS CdTe
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LDA
Expt.
4.510 5.301 5.577 6.000 5.775 6.420
4.63 5.4093 5.6676 6.101 5.832 6.477
©2009 The American Physical Society
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FIG. 1. 共Color online兲 Schematic figures of hydrogen in anion vacancy 共Vanion-H兲 with 共a兲 onefold, 共b兲 twofold, 共c兲 threefold, and 共d兲 fourfold coordinations. In 共b兲, the atoms C1 and C2 relax away from the vacancy in the donor state, 共Vanion-H兲+, but move close to each other to form a cation-cation bond in the acceptor state, 共Vanion-H兲−.
tors listed in Table I. Figure 1 shows the schematic figures of the hydrogen in the anion vacancy with coordination number ranging from 1 to 4. We first consider the single-donor state of the Vanion-H complex. H− is found to be located at the center of the O vacancy in zinc-blende ZnO 关see Fig. 1共d兲兴,
consistent with the early results for wurtzite ZnO.4,8 When the anion is changed to S, Se, or Te, we find that H− moves off center and is stabilized at the position with twofold coordination with Zn cations 关see Fig. 1共b兲兴. The energies for the structures with other H coordination numbers 共relative to the energy of the ground-state H structure of twofold coordination兲 are shown in Table II. Replacing a large anion with a much smaller one, H−, results in reduced electronic shell repulsion between the cations and H−. Thus, H− naturally moves off center to enhance the Coulomb attraction between the cations and H−. Our calculations suggest that H− finds a balance between the Coulomb attraction and the electronic shell repulsion when it approaches two Zn atoms around the anion vacancy. The Zn-H bond length is kept at about 1.77 Å for the twofold coordinated H when the host anion changes from S, Se, to Te as shown in Table II. The similar trend has also been found for CdS and CdTe, in which the twofold coordinated H is preferred in the anion vacancies with Cd-H bond length nearly unchanged for different host anions 共see Table III兲. The cation atoms that do not coordinate with H relax significantly away from the anion vacancy. We have calculated the LVMs of H in the anion vacancies of various Zn- and Cd-based II-VI semiconductors. The calculated results for the twofold coordinated H compare very well with the experimental results 共see Tables II and III兲. The calculated LVMs for three- and fourfold coordinated H are significantly lower than the experimental values due to the weaker bonding. We note that, for ZnS, the calculated LVM for onefold coordinated H 共1295 cm−1兲 is closer to the experimental value 共1325 cm−1兲 than that for the twofold coordinated H 共1252 cm−1兲. But the onefold coordinated H is metastable. Also, the trend that the measured cation-H LVM
TABLE II. Energies, Zn-H bond lengths, and the H local vibrational modes 共LVMs兲 for 共Vanion-H兲+ complexes in Zn-based II-VI semiconductors in zinc-blende structure. The experimental LVMs are found in Ref. 29. The energies of various 共Vanion-H兲+ structures for each material are relative to that of the most stable one. LVM 共cm−1兲 Coordination number
Energy 共eV兲
dCd-H 共Å兲
Theory
2.000
723
ZnO
4
ZnS
1 2 3 4
0.17 0 0.16 0.34
1.672 1.765 2.033 2.293
1295 1252 673 341
ZnSe
1 2 3 4
0.21 0 0.29 0.55
1.627 1.767 2.063 2.365
1447 1231
ZnTe
1 2 3 4
0.18 0 0.48 0.82
1.591 1.772 2.215 2.487
1588 1192
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1325
1315
1215
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TABLE III. Energies, Cd-H bond lengths, and the local vibrational modes 共LVMs兲 for 共Vanion-H兲+ complexes in Cd-based II-VI semiconductors in zinc-blende structure. The experimental LVMs are found in Ref. 29. The energies of various 共Vanion-H兲+ structures for each material are relative to that of the most stable one. LVM 共cm−1兲 Coordination number
Energy 共eV兲
dCd-H 共Å兲
Theory
CdS
1 2 3 4
0.20 0 0.10 0.31
1.836 1.911 2.137 2.402
1201 1228
CdTe
1 2 3 4
0.26 0 0.36 0.77
1.748 1.915 2.207 2.578
in the II-VI semiconductors decreases with increasing anion size is consistent with the calculated LVMs for the twofold coordinated H in the anion vacancies but not with the onefold coordinated H. The Zn-H and Cd-H bonds in the anion vacancies of II-VI semiconductors have mainly ionic character. Here we want to emphasize that the concepts of ionicity and charge transfer are extremely useful in understanding chemical bonding and the electronic structure of materials. In particular, for defects in semiconductors, the basic knowledge of chemical bonding 共e.g., ionic vs covalent兲 is very useful for understanding defect structures and determining the charge states of defect complexes. However, the concepts of ionicity and charge transfer suffer from a certain ambiguity due to the difficulty in portioning charge in a solid. In this context, a helpful approach to analyzing charge transfer is to compare the calculated properties with what would be expected under various assumed models for charge states. To begin with we consider the density-functional charge distribution of a neutral nonspin-polarized H atom in comparison with an H− ion.15 The charge distribution and the integral of the charge within a given radius are shown in Fig. 2. As may be seen the charge distributions and the integrals of the charge are quite different over the range shown. Considering H embedded in a solid, there will be a contribution to the density from neighboring atoms around H. However, unlike the charge density of an H or H− s state, which is maximum at the nucleus and falls off monotonically with distance, the contribution from neighboring atoms will be largest near those atoms and will fall off approximately exponentially as one moves away from them to the location of H. Therefore one can separate out this contribution by focusing on the charge density within small spheres centered at the H site. In the present work, we analyze the charge state of H using the charge within a small sphere of radius 1.2 bohr⬃ 0.635 Å. The charges contained in such a sphere are 0.37e and 0.51e, for neutral H and the H− ion 共Fig. 2兲. For comparison, the charge integration within the sphere of radius of 1.2 bohr around H in the anion vacancy yields 0.506e 共ZnO兲, 0.523e 共ZnS兲, 0.521e 共ZnSe兲, 0.518e 共ZnTe兲, 0.504e 共CdS兲, and 0.502e 共CdTe兲, which are in good agreement with the result
1188
Experiment
1265
1205
for the H− ion. We have also calculated the charge inside spheres of other radii for H in the S vacancy of ZnS and plotted these values in Fig. 2. As may be seen the values and the radial dependence of the charge near the H nucleus agree well with those obtained for the H− ion, and that the charge is substantially larger than that for an H atom. One may also note a deviation above either curve for larger sphere radii. This reflects the contribution from tails of other atoms. The four cation atoms around an anion vacancy can possibly form one or two cation-cation bonds. This was first pointed out by Chadi16,17 for a series II-VI and III-V semiconductors and was also discussed later by other authors.18–20 The consequence of cation-cation bond formation in an anion vacancy is that an anion vacancy in zincblende lattice can possibly take Td 共no cation-cation bond兲, C2v 共one cation-cation bond兲, or D2d 共two cation-cation bonds兲 symmetry. These three structures correspond to stable
FIG. 2. 共Color online兲 Integration of the electrons, q共r兲, within spheres around an isolated H− ion 共solid red curve兲, an isolated neutral atom 共dash blue curve兲, and H in the S vacancy of ZnS 共green cross兲 as a function of the radius 共r兲 of the sphere. Inset shows 4r2共r兲 as a function of r, where 共r兲 is the electron density.
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MAO-HUA DU AND DAVID J. SINGH TABLE IV. Zn-H, Zn-Zn bond lengths, and the H local vibrational modes 共LVMs兲 of 共Vanion-H兲− complexes in Zn-based II-VI semiconductors.
ZnS ZnSe ZnTe
dZn-H 共Å兲
dZn-Zn 共Å兲
LVM 共cm−1兲
1.686 1.710 1.743
2.418 2.423 2.435
1620 1497 1322
defect charge states of +2, 0, and −2 for II-VI semiconductors and their relative stability depends on the Fermi level. This is true for most of the II-VI semiconductors except for the case with a small anion. For instance, in ZnO, the dimerization of the cations around O vacancy was not found.19 The insertion of H in the O vacancy of ZnO results in a fourfold coordinated H. In other II-VI semiconductors under this study, the insertion of H in the anion vacancy still allows the formation of one cation-cation bond but prevents the formation of the second cation-cation bond as H is coordinated with two cations. The Vanion-H complex in the II-VI semiconductors studied here can either be a single-electron donor or acceptor. When 2+ 共no cation-cation the Fermi level is low, H− binds with Vanion bond兲, resulting in a single-electron donor with two cations coordinated with H− while the other two 关labeled C1 and C2 in Fig. 1共b兲兴 relax away from the vacancy. When the Fermi 0 关one cation-cation bond level is high, H− binds with Vanion between atoms C1 and C2 in Fig. 1共b兲兴, resulting in a singleelectron acceptor. In 共Vanion-H兲−, the accumulated electrons along the cation-cation bond repel the H− ion, resulting in shorter cation-H bonds and higher H LVMs, as shown in Tables IV and V. VO-H in ZnO only exists as a donor since no Zn-Zn bond can be formed. For most of the other II-VI semiconductors with zinc-blende structure, Vanion-H is amphoteric. Figure 3 shows the 共+ / −兲 transition level within the band gap for Vanion-H in various II-VI semiconductors. The amphoteric behavior is also expected for these semiconductors in wurtzite structure. Interestingly, the 共+ / −兲 transition levels for Vanion-H in Fig. 3 are roughly lined up in absolute scale within half electron volt. The 共+ / −兲 transition level is the Fermi level at which the energies of 共Vanion-H兲+ and 共Vanion-H兲− are equal to each other. The energy difference between 共Vanion-H兲+ and 共Vanion-H兲− is largely determined by the energy difference between the empty cation dangling-bond orbital and the filled cation-cation bonding orbital. The Zn-Zn bond lengths for ZnS, ZnSe, and ZnTe are approximately the same as shown in Table IV, justifying the close alignment of the TABLE V. Cd-H, Cd-Cd bond lengths, and the H local vibrational modes 共LVMs兲 of 共Vanion-H兲− complexes in Cd-based II-VI semiconductors.
CdS CdTe
dCd-H 共Å兲
dCd-Cd 共Å兲
LVM 共cm−1兲
1.845 1.888
2.736 2.742
1563 1313
TABLE VI. Energies and cation-H bond lengths of 共Vanion-F兲+ complexes in ZnS and CdTe. The energies of various 共Vanion-F兲+ structures for each material are relative to that of the most stable one.
Coordination number
Energy 共eV兲
dcation-F 共Å兲
ZnS
1 2 3 4
0.06 0.03 0 0.07
2.143 2.048 2.154 2.316
CdTe
1 2 3 4
0.27 0 0.03 0.28
2.241 2.186 2.364 2.576
共+ / −兲 levels among the Zn-based compounds. In addition, the electronegativities of Zn 共1.65兲 and Cd 共1.69兲 are nearly same. This may explain the closeness of the 共+ / −兲 transition levels for Vanion-H in the Zn-based and Cd-based II-VI semiconductors. The 共+ / −兲 transition levels for the interstitial H in various semiconductors and insulators have also been found to be roughly aligned.21 However, for the interstitial H, the 共+ / −兲 transition level is largely determined by the energy difference between the empty cation dangling-bond level and the filled anion dangling-bond level.21 IV. DISCUSSION
It is often useful to analyze structures of ionic compounds in terms of ionic radii.22 In particular, bond lengths in halides and ionic chalcogenides rarely deviate by more than a few percent from the values indicated by the ionic radii and, furthermore, when there are large deviations it is often indicative of interesting hybridization effects as in, e.g., Pb containing perovskites such as PbTeO3, where Pb-O hybridization stabilizes ferroelectricity. However, H− is a particularly flexible ion, i.e., the variability in its bond lengths is larger than for halide anions and consistent ionic radii for H− are therefore not tabulated.22–24 However, in an ionic hydride with low-electronegativity metals, H− often behaves similarly to F− from a structural point of view.25–27 For instance, the LiH lattice constant 共4.083 Å兲 is nearly the same as that for LiF 共4.027 Å兲. Our calculations on the structures of H and F in the anion vacancy of ZnS and CdTe show that H and F behave similarly as anions except for different cation-H and cation-F bond lengths 共see Tables II, III, and VI兲. In the S vacancy of ZnS, the longer Zn-F bond length results in the threefold coordinated F rather than the twofold coordinated one adopted by H. The shorter cation-H bond compared to the cation-F bond indicates some degree of hybridization between the H states and the host states. The Zn- and Cd-based II-VI semiconductors studied here are not purely ionic materials. The Ewald field that stabilizes the H− ion is stronger in ionic hosts and weaker in more
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FIG. 3. 共Color online兲 Calculated 共+ / −兲 levels for Vanion-H complex in several II-VI semiconductors. For each semiconductor, the lower and upper black lines indicate the valence and conductionband edges, respectively. The red line indicates the 共+ / −兲 transition level for the Vanion-H. The valence-band offset is taken from Ref. 29. The conduction-band edges are shifted to reflect to the experimental band gaps.
covalent hosts. As such, the H− in an anion vacancy of a more covalent host will also tend to be more hybridized even if the chemical species of the nearest-neighbor cations are the same as in ZnTe in comparison with ZnO. Figure 4 shows the projected density of states 共PDOS兲 for the hydrogen s orbital in the anion vacancies of ZnO and ZnTe. The high-energy part of the H PDOS 关e.g., the PDOS peak 共⬎5 eV兲 in Fig. 4共a兲兴 is largely the H 2s state and its resonance with the conduction-band states. There is small H 1s contribution near the conduction-band edge, which is the result of the covalent type of hybridization between the filled H 1s and empty Zn 4s states. It is noticeable that the hybridization between H and the host band states in ZnTe is en-
hanced compared to that in ZnO because ZnTe is more covalent than ZnO and the Te states in ZnTe are much more dispersive than the O states in ZnO. Our calculations show that the maximum valence electron density near H is higher than that near Te in ZnTe but lower than that near O in ZnO, reflecting the increasing electronegativity from Te, H, to O. The fact that the Zn and Cd atoms can make cation-cation covalent bonds in the anion vacancy for the acceptor structure of Vanion-H 共except for oxides兲 indicates some degree of covalency in the system. In highly ionic materials, the formation of the cation-cation covalent bond is unlikely for highly electropositive cations regardless of the anion size, thereby rendering Vanion-H only stable as a shallow donor. We have also calculated the H structures in the As vacancy of GaAs, a more covalent semiconductor. We find that H in 共VAs-H兲2+ is onefold coordinated, forming a single covalent bond with a nearby Ga atom. Clearly, the ionicity of the host material has a critical effect on the bonding of H in the vacancy. Finally, we want to point out that multicoordination that is incompatible with the number of available electron pairs is usually the indication of ionic bonding in compounds with cations and anions of very different electronegativities. It can also be the result of metallic bonding if the atoms in the system have similar electronegativities. In an ionic crystal or a highly polar semiconductor, it is the electronic shell repulsion that causes the multicoordination of H in anion vacancies, while the absence of such repulsion results in the absence of multicoordination for the H in cation vacancies. In a cation vacancy, H is usually a donor, H+. Without an electron shell, H+ can move deeper into the electron shell of the anion atom until the Coulomb attraction is screened out. Thus, H+ usually binds with only one anion atom in the cation vacancy such as the case for H in Cd vacancy of CdTe.20 Also, the anion-H bond length is often shorter than the ionic radius of the anion. V. CONCLUSIONS
FIG. 4. Density of states projected on the s orbital of hydrogen in anion vacancies of 共a兲 ZnO and 共b兲 ZnTe.
We study the structure, the nature of bonding, and the local vibrational modes for hydrogen in anion vacancies of various Zn- and Cd-based II-VI semiconductors. Our results show that, in polar semiconductors with relatively high ionicity, hydrogen in an anion vacancy is anionic as H− ion with multicoordination. The coordination number depends on the anion size. In all the II-VI semiconductors we have studied, i.e., ZnX 共X = O, S, Se, and Te兲 and CdX 共X = S and Te兲, H always takes a twofold coordinated structure in the anion vacancy except for ZnO in which H is a fourfold coordinated in the O vacancy. On the other hand, in the anion vacancies of more covalent semiconductors such as GaAs, hydrogen prefers to form a single covalent bond with a cation atom around the anion vacancy. Our results also suggest that, in the zinc-blende and wurtzite II-VI semiconductors, the Vanion-H complex is usually amphoteric, either being a 2+ 兲 or being a single-electron single-electron donor 共H− in Vanion acceptor 共H− in neutral Vanion with a cation-cation bond in the vacancy兲. The exception occurs for the semiconductors with small anion size and high anion electronegativity, such as
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ZnO and GaN, etc., in which Vanion-H acts only as shallow donor because the anion vacancy is too small to accommodate both an H− ion and a cation-cation bond needed for the acceptor structure.
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ACKNOWLEDGMENTS
This work was supported by the U.S. DOE Office of Nonproliferation Research and Development NA22.
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